Using XMM-Newton spatially resolved X-ray imaging spectroscopy we obtain the temperature, density, entropy, gas mass, and total mass profiles for two groups of galaxies out to approximately 0.3 R(sub vir)(R(sub vir), the virial radius). Our density profiles agree well with those derived previously, and the temperature data are broadly consistent with previous results but are considerably more precise. Both of these groups are at the mass scale of 2x10(exp 13) M(solar mass), but have rather different properties. Both have considerably lower gas mass fractions at r < 0.3 R(sub vir), than the rich clusters. NGC2563, one of the least luminous groups for its X-ray temperature, has a very low gas mass fraction of approximately 0.004 inside 0.1 R(sub vir), which increases with radius. NGC4325, one of the most luminous groups at the same average temperature, has a higher gas mass fraction of 0.02. The entropy profiles and the absolute values of the entropy as a function of virial radius also differ, with NGC4325 having a value of approximately 100 keV cm(exp -2) and NGC2563 a value of approximately 300 keV cm(exp -2) at r approximately 0.1 R(sub vir). For both groups the profiles rise monotonically with radius and there is no sign of an entropy 'floor'. These results are inconsistent with pre-heating scenarios that have been developed to explain a possible entropy floor in groups, but are broadly consistent with models of structure formation that include the effects of heating and/or the cooling of the gas. The total entropy in these systems provides a strong constraint on all models of galaxy and group formation, and on the poorly defined feedback process that controls the transformation of gas into stars and thus the formation of structure in the universe.